I’m no expert but I think the best practice is generally to keep the backup codes in a non-electronic format in a secure location, such as on paper stored in a fireproof safe or a bank’s safe deposit box. You wouldn’t forget that location. It’s not a cheap solution, though, and a safe deposit box limits you to the bank’s operating hours only. Using your backup code is typically pretty rare, though.
I would not use the TOTP offered by your password vault, though, especially if the vault backs up to multiple devices or the cloud.